Kyoto Journal of Mathematics

Classification of automorphisms on a deformation family of hyper-Kähler four-folds by p-elementary lattices

Samuel Boissière, Chiara Camere, and Alessandra Sarti

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Abstract

We give a classification of all nonsymplectic automorphisms of prime order p acting on irreducible holomorphic symplectic four-folds deformation equivalent to the Hilbert scheme of two points on a K3 surface, for p=2,3, and 7p19. Our classification relates some invariants of the fixed locus to the isometry classes of two natural lattices associated to the action of the automorphism on the second cohomology group with integer coefficients. In several cases we provide explicit examples. As an application, we find new examples of nonnatural nonsymplectic automorphisms of order 3.

Article information

Source
Kyoto J. Math., Volume 56, Number 3 (2016), 465-499.

Dates
Received: 24 March 2014
Revised: 22 April 2015
Accepted: 23 April 2015
First available in Project Euclid: 22 August 2016

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1471872277

Digital Object Identifier
doi:10.1215/21562261-3600139

Mathematical Reviews number (MathSciNet)
MR3542771

Zentralblatt MATH identifier
1375.14143

Subjects
Primary: 14J50: Automorphisms of surfaces and higher-dimensional varieties
Secondary: 14C05: Parametrization (Chow and Hilbert schemes) 03G10: Lattices and related structures [See also 06Bxx]

Keywords
irreducible holomorphic symplectic manifolds Hilbert scheme automorphisms special lattices classification

Citation

Boissière, Samuel; Camere, Chiara; Sarti, Alessandra. Classification of automorphisms on a deformation family of hyper-Kähler four-folds by $p$ -elementary lattices. Kyoto J. Math. 56 (2016), no. 3, 465--499. doi:10.1215/21562261-3600139. https://projecteuclid.org/euclid.kjm/1471872277


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